Bergdahl, 28, was released from captivity May 31 after nearly five years as a prisoner of the Taliban in Afghanistan. The U.S. Army soldier was freed in exchange for five Guantanamo terrorism detainees. He has been at the Landstuhl Regional Medical Center in Germany since shortly after his release from captivity.

The Idaho man's post-captivity reintegration process entails three phases, starting with recovery. The program was developed from lessons learned after the release of prisoners of war following the Vietnam War.

The second phase of reintegration has taken place at Landstuhl, where Bergdahl has been receiving medical care and briefings with psychologists. Pentagon officials have said in recent days that his health has continued to improve and that he has been "engaging with hospital staff more and more each day."

Officials had said that there was no specific timetable for how long Bergdahl would remain at Landstuhl.

"Nobody is going to push it any further or any faster than Sgt. Bergdahl and his caregivers are willing to take it," Kirby said at a Tuesday briefing. "This soldier was held captive for nearly five years in what we must assume were harsh conditions. He's going to need time to reassimilate, time to heal mentally and physically."

It was also up to Bergdahl to decide when he might make contact with his parents, and, as of Thursday, Defense officials said he had still not spoken with his family. The third phase of reintegration in San Antonio includes a reunion with family members.

The Obama administration has come under fire for not giving U.S. lawmakers a heads-up about the release, but Secretary of Defense Chuck Hagel told a House committee Wednesday that the exchange was too delicate, too uncertain and too fast-moving for him to have alerted Congress beforehand, as some have said the law requires.